In this article we propose to analyze over-dispersed panel count data using a Gamma-Frailty nonhomogeneous Poisson process model. Conditional on a Gamma distributed frailty variable, the cumulative count, N (t), is assumed to follow a nonhomogeneous Poisson process. Cubic B-spline functions are used to approximate the logarithm of the baseline mean function Λ0 (t) in the semiparametric proporti...

In this paper we examine the claims reserving problem using Tweedie’s compound Poisson model. We develop the maximum likelihood and Bayesian Markov chain Monte Carlo simulation approaches to fit the model and then compare the estimated models under different scenarios. The key point we demonstrate relates to the comparison of reserving quantities with and without model uncertainty incorporated ...

Compound Poisson population models are particular conditional branching process models. A formula for the transition probabilities of the backward process for general compound Poisson models is verified. Symmetric compound Poisson models are defined in terms of a parameter θ ∈ (0,∞) and a power series φ with positive radius r of convergence. It is shown that the asymptotic behavior of symmetric...

BACKGROUND Continued automobile driving is important for the wellbeing and independence of older adults. Frailty has been associated with a variety of negative health outcomes, but studies are lacking on the potential association between frailty and driving status. The present study uses data from The National Health and Aging Trends Study (NHATS) to assess if the presence of frailty is associa...

In this note we study the optimal dividend problem for a company whose surplus process, in the absence of dividend payments, evolves as a generalized compound Poisson model in which the counting process is a generalized Poisson process. This model includes the classical risk model and the Pólya-Aeppli risk model as special cases. The objective is to find a dividend policy so as to maximize the ...

The parameter estimation for the Compound Poisson Software Reliability Model is analyzed. The biased characteristic is considered in order to get better performance. A comparison with the well known Non Homogeneous Software Reliability Models is presented. Several experimental data are used in order to analyze the goodness of fit of both models.

In this paper, we consider a perturbed compound Poisson risk model with two-sided jumps. The downward jumps represent the claims following an arbitrary distribution, while the upward jumps are also allowed to represent the random gains. Assuming that the density function of the upward jumps has a rational Laplace transform, the Laplace transforms and defective renewal equations for the discount...

Abstract. We present a Bayesian analysis for recurrent events data using a nonhomogeneous mixed Poisson point process with a dynamic subject-specific frailty function and a dynamic baseline intensity func- tion. The dynamic subject-specific frailty employs a dynamic piecewise constant function with a known pre-specified grid and the baseline in- tensity uses an unknown grid for the piecewise ...

In this paper we examine the claims reserving problem using Tweedie’s compound Poisson model. We develop maximum likelihood and Bayesian Markov chain Monte Carlo simulation approaches to fit the model and then compare estimated models under different scenarios. The key point we demonstrate relates to comparison of reserving quantities with and without model uncertainty incorporated into the pre...